My sister was born in England and her father was a military serviceman. She holds US recognized dual citizenship. She is also a natural born citizen, by law and by the First Congress’s definition, regardless of the fact that England grants her citizenship.
The fact that you had to say ‘by law’ nullifies the natural part of natural born.
By the immigration act passed by the first Congress a child born to US citizens overseas ‘was considered’ a ‘natural born Citizen’ (note that the wording, capitalization exactly matched Article II, Section 1. No hyphen, capital C). So the intent of that act was just as you describe to grant, via law, natural born status to those born overseas to citizen parents (note that is it is plural).
Unfortunately for your sister, assuming she has plans to make a run on the US Presidency, the next version of the immigration dropped that passage. And thus, there is no law and has not been for 200 years that declares a person born to US Citizens (such as John McCain) a natural born Citizen according to Article II, Section 1.
Notice that the law even acknowleges that a person born overseas to US Citizens is not a natural born Citizen. The law made them legally equal with declearing them an actual natural born Citizen. Those in the category were CONSIDERED AS. This is because natural born Citizen is not a legal construct. It is a construct that is considered part of natural law and beyond the controls of ordinary man-made law. So the founders never attempted to define something they considered a non-legal issue. And when they knew they wanted sons borh overseas eligible for the Presidency they did make make a law to have them CONSIDERED AS natural born Citizens - because they knew - they were not.
But then they removed the passage. Likely because they realized the had illegally attempted to alter the base Constitution in a non-Constitutional manner.